Studying the relative orientations of the orbits of exoplanets and wide-orbiting binary companions (semimajor axis greater than 100 au) can shed light on how planets form and evolve in binary systems. Previous observations by multiple groups discovered a possible alignment between the orbits of visual binaries and the exoplanets that reside in them. In this study, using data from Gaia DR3 and TESS, we confirm the existence of an alignment between the orbits of small planets (R < 6 R⊕) and binary systems with semimajor axes below 700 au (p = 10‑6). However, we find no statistical evidence for alignment between planet and binary orbits for binary semimajor axes greater than 700 au and no evidence for alignment of large, closely orbiting planets (mostly hot Jupiters) and binaries at any separation. The lack of orbital alignment between our large-planet sample and their binary companions appears significantly different from our small-planet sample, even taking into account selection effects. Therefore, we conclude that any alignment between wide binaries and our sample of large planets (predominantly hot Jupiters) is probably not as strong as what we observe for small planets in binaries with semimajor axes less than 700 au. The difference in the alignment distribution of hot Jupiters and smaller planets may be attributed to the unique evolutionary mechanisms occurring in systems that form hot Jupiters, including potentially destabilizing secular resonances that initiate as the protoplanetary disk dissipates and high-eccentricity migration occurring after the disk is gone.